Riemannian Geometry and Geometric Analysis (Universitext) - Softcover

J�rgen Jost

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9783540259077: Riemannian Geometry and Geometric Analysis (Universitext)

Softcover

ISBN 10: 3540259074 ISBN 13: 9783540259077

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 2005

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This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. Besides several smaller additions, reorganizations, corrections, and a systematic bibliography, the main new features of the 4th edition are a systematic introduction to K�hler geometry and the presentation of additional techniques from geometric analysis.

From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry, e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. [..] The book is made more interesting by the perspectives in various sections." Math. Reviews

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From the Back Cover:

This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition already introduced and explained the ideas of the parabolic methods that had found a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discussed further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry.

The 6th edition includes a systematic treatment of eigenvalues of Riemannian manifolds and several other additions. Also, the entire material has been reorganized in order to improve the coherence of the book.

From the reviews:
"This book provides a very readable introduction to Riemannian geometry and geometric analysis. ... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome." Mathematical Reviews

"...the material ... is self-contained. Each chapter ends with a set of exercises. Most of the paragraphs have a section ‘Perspectives’, written with the aim to place the material in a broader context and explain further results and directions." Zentralblatt MATH

About the Author:

J�rgen Jost is Codirector of the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, an Honorary Professor at the Department of Mathematics and Computer Sciences at Leipzig University, and an External Faculty Member of the Santa Fe Institute for the Sciences of Complexity, New Mexico, USA.

He is the author of a number of further Springer textbooks including Postmodern Analysis (1997, 2002, 2005), Compact Riemann Surfaces (1997, 2002, 2006), Partial Differential Equations (2002, 2007), Differentialgeometrie und MInimalfl�chen (1994, 2007, with J. Eschenburg), Dynamical Systems (2005), as well as several research monographs, such as Geometry and Physics (2009), and many publications in scientific journals.

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